KPROJ: A program for unfolding electronic and phononic bands

We introduce a program named KPROJ that unfolds the electronic and phononic band structure of materials modeled by supercells. The program is based on the k-projection method, which projects the wavefunction of the supercell onto the k-points in the Brillouin zone of the artificial primitive cell. It allows for obtaining an effective “local” band structure by performing partial integration over the k-projected wavefunctions, e.g., the unfolded band structure with layer-projection for interfaces and the weighted band structure in the vacuum for slabs. The layer k-projection is accelerated by a scheme that combines the Fast Fourier Transform (FFT) and the inverse FFT algorithms. It is now interfaced with several first-principles codes based on plane waves such as VASP, Quantum Espresso, and ABINIT. In addition, it also has interfaces with ABACUS, a first-principles simulation package based on numerical atomic basis sets, and PHONOPY, a program for phonon calculations.

Program summary

Program Title: KPROJ

CPC Library link to program files: https://doi.org/10.17632/f6n5phpy8f.1

Developer's repository link: https://github.com/mxchen-2020/kproj

Licensing provisions: GPLv3.0

Programming language: Fortran 90

Nature of problem: Supercells are widely used to model doped systems and interfaces within the framework of first-principles methods. However, the use of supercells causes band folding, which is unfavorable for understanding the effects of doping and interfacing on the band structure of materials. Moreover, the folding also brings difficulties in explaining the results of angle-resolved photoemission spectroscopy experiments.

Solution method: This program is designed to calculate the unfolded band structure for systems modeled by supercells. The unfolding is performed by projecting the wave functions of the supercell onto the k-points in the BZ of the primitive cell. The projector operator is built by the translation operator and its irreducible representation. The layer k-projected band structure is obtained by integrating the projected wave function in a selected spatial window, for which the FFT and inverse FFT algorithms are used to accelerate the calculation.